Gearing tooth form

ABSTRACT

The invention concerns a morphology matrix for forming the cross-sectional shape of a short gearing tooth, in particular on toothed wheels of motor vehicle gearboxes. The short gearing teeth are formed on a cylindrical section of a gear wheel or gear shift sleeve, the axis of this section coinciding with the displacement axis of the gear shift sleeve. Each tooth comprises a tip which is chamfered in roof-like manner and has lateral flanks ( 3 ) which are shaped towards the tooth base ( 1 ) so that they have a relief at least over part of their height. The lateral flanks ( 3 ) terminate in a radiused tooth base ( 4 ), all of the teeth, or some thereof defined according to a regularly changing pattern, having at least a morphology defining the shape of the lateral flanks.

The invention concerns a morphology matrix for forming thecross-sectional shape of a short gearing tooth, in particular on toothedwheels of motor vehicle gearboxes, the short gearing teeth being formedon a cylindrical section of a gear wheel or gear wheel sleeve, the axisof this section coinciding with the displacement axis of the gear shiftsleeve, each tooth comprising a tip which is chamfered in a roof-likemanner and lateral flanks which terminate in a radiused tooth base andcomprise an undercut section that extends at least over part of theflank height.

The above-mentioned short gearing morphology is described in therelevant technical literature and has been translated into practice.

An essential characteristic to be achieved in a short gearing systemconsists in the smoothest possible shifting between two gear wheelsalready moving synchronously, i.e. in limiting friction to an absoluteminimum; especially reducing the occurrence and duration of frontalcontact between the gear tips of two short gearing units. However,neither axial contact nor the safe axial stability of the selectedgearshift mechanism may be sacrificed in favor of such shifting comfort.Instead, specially shaped lateral tooth flanks are used, the toothflanks comprising an undercut section so that at least part of thelateral tooth flank tapers towards the tooth base. Two correspondinginteracting short gearing units thus designed ensure that neighboringundercut lateral tooth flanks are appropriately protected against axialdisplacement and the resulting undesired undoing of the shiftingconnection.

The expert is familiar with the fact that individual teeth in aconventionally designed short gearing system are over their entireheight attached to a cylindrical section and can also be attached to abase. Additionally, the expert is familiar with the fact that a radiusedtooth base can improve the resistance of the teeth and that roof-likechamfering of the tooth tip can facilitate the meshing of the teeth.

However, as there are many different possibilities for application ofshort gearing systems which are characterised by different loads andload changing patterns and as different shifting comfort and shiftingsafety requirements must be met in practice, also requiring a number ofcriteria in connection with the metal forming method to be met, it canbe assumed that the expert will usually find it difficult to identifythe most appropriate solution for every single case.

In view thereof, one of the objectives of the present invention consistsin providing an overview of the layout and design criteria for shortgearing units, i.e. in offering the expert a means by which he caneasily and reliably identify the solutions meeting the applicablerequirements in every specific case.

The proposed invention is not limited to the identification of a singlesolution for each case but consists of a morphology matrix for theadequate designing of the cross-sectional shapes of short gearing teeth.

Additionally, the morphology matrix mentioned above is characterised bythe fact that all teeth or a part thereof defined according to aregularly changing pattern are characterised by at least one of the twofollowing features defining the design of the lateral tooth flanks:

a) Between the lower edge of the tooth roof surface of the tooth tip andthe undercut section of the tooth flank an upper spur toothing sectionin the shape of a guiding surface (flat) largely parallel to thelongitudinal axis of the tooth is provided, the guiding surface beingeither narrow or wide.

b) Between the undercut section of the tooth flank and the radiusedtooth base a lower spur toothing section is provided in the form of atooth base reinforcement with a supporting surface largely parallel tothe longitudinal axis of the tooth, the supporting surface being eitherlow or high.

The matrix which constitutes the object of the present invention isbased on the assumption that said invention facilitates, in addition tothe undercut flank section, depending on a specific application, one ortwo spur gear sections in particular, consisting of additional sectionson each lateral flank, namely either an upper spur toothing sectionabove the undercut section of the flank and/or a lower spur toothingsection below the undercut section of the flank.

The upper spur toothing section constitutes a guiding surface, alsocalled “flat”, which becomes effective when the teeth begin to engageand reinforces, in the initial contact area, the most lateral sectionsof the flank, thus prolonging the service life of the toothing. Theguiding surfaces reduce the so-called “backlash”, i.e. the forcesoccurring as a response to the shifting movement are reduced withoutincreasing the face clearance.

The guiding surfaces can be narrow or wide (seen in the longitudinaldirection of the tooth). The guiding surface (5) of the first width,measured in the direction of the tooth height can measure less than onesixth of the remaining height of the tooth tip above. The guidancesurface (6) of the second width measured in the direction of the toothheight, may be shorter than the overall tooth height, but longer thanhalf of the remaining height of the tooth tip above. The choice betweennarrow and wide guiding surfaces has a significant impact on the size ofthe relief angle of undercut because a wide guiding surface implies alarger and, thus, more effective relief angle than a narrow guidingsurface. At the same time, the width of the guiding surface must beconsidered a function of the load, i.e. of the occurring torques.

However, the teaching of the present invention is not limited to anupper spur toothing section only. Instead, a lower spur toothing sectionlocated below the undercut flank section can be provided in addition toor instead of the upper spur toothing section. The lower spur toothingsection reinforces the tooth base, consisting of a supporting surfaceparallel to the longitudinal axis of the tooth which counteracts thetapering of the tooth caused by the undercut tooth section. This kind ofsupporting surface thus directly increases the strength of the entiretooth, especially of the portion near the tooth base.

In cases where particularly high torque loads occur those learned in theart will, within the limits of the morphology proposed in the frameworkof the invention, combine an upper and a lower spur toothing section inorder to benefit from a combination of both guiding surfaces andsupporting surfaces.

The supporting surface of each tooth flank can be either high or low.The choice between high or low will mainly depend on the relief anglechosen by the expert.

If only one upper spur toothing section—with a narrow or wide guidingsurface—is intended, a relief angle of up to 9 angular degrees isrecommended according to the correlation 0≦α≦9.

If a lower spur toothing section with a low supporting surface—with orwithout an additional upper spur toothing section—is provided, a reliefangle between 3 and 12 angular degrees is recommended according to thecorrelation 3≦α≦12.

If a lower spur toothing section with a high supporting surface—with orwithout an upper spur toothing section—is intended, a relief anglebetween 6 and 60 angular degrees is recommended according to thecorrelation 6≦α≦60. The largest relief angles are realised by selectingan upper spur toothing section in the form of a wide guiding surface anda lower spur toothing section in the form of a high supporting surface.

Supporting surface (7) of the low type, measured from the tooth base canbe wider than the guiding surface of the wide type but is lower thanhalf the tooth height measured from the tooth base (1) to the lower edgeof the roof surface. The supporting surface (8) of the high type,measured from the tooth base, is approximately half as long as theoverall tooth height. These rules can be derived on the basis of theoverall geometry and are only valid when teeth with an identical overalltooth height or tooth tip height, respectively, are compared. The toothheight measured from below the tooth tip to the tooth base is the sumtotal of the guiding surface, the undercut flank section and thesupporting surface, whereas towards the bottom always follows a radiusedtooth base which can be designed with a smaller radius on teeth with asupporting surface in comparison with teeth without a supportingsurface.

As far as the shape of the roof-shaped tooth tip is concerned, it isassumed that the intended roof shapes consist of familiar shapeelements, i.e. of straight or convex roof surfaces.

The straight roof surface stands out for its durability. On the otherhand, it implies a large friction surface which means that the forcescounteracting the tooth engaging process are relatively high.

The convex roof surface implies a reduced friction force due to the factthat contact is limited to a narrow line only, which means that a highershifting comfort can be achieved.

In the case of reversible gears, i.e. gear wheels that can rotate inboth directions, only symmetrical roof shapes can be used. Forconventional non-reversible gear wheels asymmetrical roof shapes areparticularly favourable which limit the period during which significantcounterforces must be expected in the course of the engaging process.The duration of blocking, if any, during the engaging process decreasesas the shape of the tooth tip approaches a monopitch roof.

The two roof surfaces of a tooth tip can either both be plane or convexor one can be plane and one convex. The ease of meshing achieved byconvex roof surfaces can be increased in nonreversible gear wheels bymanufacturing one of the roof surfaces as a plane surface that islargely parallel to the longitudinal axis to the tooth while the otherroof surface is correspondingly pitched and forms a monopitch roof shapetogether with the first surface.

In the following the invention is explained by means of an illustrationwhich shows an image matrix.

The matrix contains nine fully occupied vertical columns and five fullyoccupied horizontal rows. The columns are numbered 1-9, the rows areallocated the letters a-e. Thus every tooth shape indicated can beclearly identified.

Row a contains two state-of-the-art tooth shapes. Column 0 contains atooth Za0 that does not extend all the way to base 1. It has asymmetrical roof shape with a plane roof surface 2 (roof shape D2, 2)and undercut lateral flanks 3 which end at a certain distance from thetooth base 1, which means that between the tooth Za0 and tooth base 1 aclearance exists for a tool used to machine the undercut lateral flanks,e.g. by offset shaping.

Tooth Za1 has the cross section of a short tooth gearing which iscovered by the preamble of claim 1, thus, like tooth Za0, is included inthe state of the art. A roof shape D2, 2 is combined with lateral flanks3 which are undercut all the way down to the tooth base 1, ending attooth base 1 with a radiused tooth base 4. In practice this kind oftooth has been manufactured by applying metal forming methods. All otherteeth described in the matrix covered by the invention can also bemanufactured by metal forming methods.

According to the systematics underlying the matrix, the tooth shapes arearranged within the rows in such a way that the relief angle increasesfrom column 1 to column 9. This is due to the choice and/or combinationof spur toothing sections. As the intention of the matrix protectedunder the present invention consists in identifying an appropriatechoice and/or combination of spur toothing sections, the tooth shapesindicated in column 1, rows b to e are not covered by the protectedobject of the invention as they include no spur toothing sections atall.

These tooth shapes are nevertheless included in the matrix forsystematic reasons so as to illustrate the different roof shapes bywhich the tooth shapes of the matrix differ from row to row.

Tooth shape Za2 differs from the state of the art according to Za1 bythe fact that an upper spur toothing section in the form of a narrowguiding surface 5 is intended. In contrast to this, tooth shape Za3 isprovided with a wide guiding surface 6.

Tooth shape Za4 differs from the tooth shapes indicated above by thefact that it comprises a lower spur toothing section in the shape of alow supporting surface 7.

Tooth shape Za5 comprises both an upper and a lower spur toothingsection in the form of a narrow guiding surface 5 and a low supportingsurface 7.

Tooth shape Za6 is characterised by a combination of a wide guidingsurface 6 and a low supporting surface 7.

Tooth shape Za7 has only a lower spur toothing section manufactured inthe form of a high supporting surface 8.

Tooth shape Za8 is characterised by a combination of a high supportingsurface 8 and a narrow guiding surface 5.

Tooth shape Za9 is characterised by a combination of a wide guidingsurface 6 and a high supporting surface 8.

The relief angle α is for each tooth shape of row a indicated above theroof shape in the respective illustration. All angles indicated merelyserve as examples for possible angles. Identical angles are indicatedfor all tooth shapes in rows b to e as the widths and lengths in theserows are identical. As indicated above, the rows only differ by thevarious roof shapes. Therefore, the individual tooth shapes need not bedescribed for every single row.

The roof shape illustrated in row b is spherical, i.e. the tip consistsof two convex roof surfaces 9 which, combined into a roof tip like allother specified roof shapes, yield a rounded tip. The roof shapes D2, 2in row a and D9, 9 in row b are symmetrical; they are suitable for gearwheels that will actually or can be rotated in both directions. Incontrast to roof shape D2,2, roof shape D9,9 is characterised by thefact that the contact with an interlocking toothed unit is limited to aline, thus facilitating the meshing of the teeth in comparison with roofshape D2,2.

Rows c, d and e illustrate asymmetrical roof shapes. Row c contains roofshape D2, 9 in which the engaging of the teeth on the side of the convexroof surface 9 is facilitated. If the interlocking gear wheel ismanufactured inversely, the manufacturing process is facilitated by thefact that both gear wheels can be manufactured with one plane roofsurface which can be manufactured more easily.

Row d contains a roof shape that resembles a monopitch roof, theinclined roof surface being manufactured as plane roof surface 10. Thesecond roof surface 11 is parallel to the longitudinal tooth axis.Similarly, row e also contains a monopitch roof, the inclined roofsurface 12 however being convex. This type of asymmetrical monopitchroof shapes can only be used for gear wheels, which rotate in only onedirection. The advantage of the monopitch roof shape consists in thefact that the probability of frontal contact during the meshing issignificantly reduced as the engaging of the teeth can only be blockedwithin a small marginal section of the monopitch roof shape.

As a matter of course, the asymmetrical roof shapes illustrated in rowsc to e can also be mirror-inverted in relation to the longitudinal toothaxis. The matrix can, within the framework of the current invention, beeven extended by selecting other roof shapes or by varying thegeometrical properties as far as the tooth height is concerned.

What is claimed is:
 1. A short gearing tooth, for use in particular ontoothed wheels of motor vehicle gearboxes, said gearing toothcomprising: a tooth height defined between a tooth base and a tooth tipas viewed along the longitudinal axis of the tooth, said tip beingchamfered to form a roof surface having a lower surface, lateral flanks,which are undercut over at least part of their height measured along thelongitudinal axis of the tooth, tapering towards the tooth base therebyforming a relief angle ending in a radiused tooth base, a guidingsurface having an upper terminus and a lower terminus and a widthdefined therebetween as measured along the longitudinal axis of thetooth, said guiding surface being formed on said lateral flanks betweenthe lower edge of the roof surface and the undercut section of thelateral flanks and being largely parallel to the longitudinal axis ofthe tooth, said guiding surface width being smaller than the distancealong the longitudinal axis of the tooth from the upper terminus of theguiding surface to the tooth tip, and a supporting surface having alower terminus and an upper terminus and a width formed therebetween,said supporting surface being formed between the undercut section of thelateral flanks and the radiused tooth base and largely parallel to thelongitudinal axis of the tooth.
 2. A short gearing tooth according toclaim 1, wherein said relief angle amounts to up to 9 angular degrees.3. A short gearing tooth according to claim 1, wherein said relief angleis between 3 and 12 angular degrees.
 4. A short gearing tooth accordingto claim 1, wherein said relief angle is between 6 and 60 angulardegrees.
 5. A short gearing tooth according to claim 1, wherein thewidth of the guiding surface measures less than one-sixth of thedistance along the longitudinal axis of the tooth from the upperterminus of the guiding surface to the tooth tip.
 6. A short gearingtooth according to claim 1, wherein the width of the guiding surface isless than the tooth height but greater than half of the distance alongthe longitudinal axis of the tooth from the upper terminus of theguiding surface to the tooth tip.
 7. A short gearing tooth according toclaim 1, wherein the width of the supporting surface is larger than thewidth of the guiding surface and smaller than the distance along thelongitudinal axis of the tooth from the tooth base to the lower surfaceof the roof surface (or alternatively “to the upper terminus of theguiding surface”).
 8. A short gearing tooth according to claim 1,wherein the width of the supporting surface is approximately half aslong as the tooth height.
 9. A short gearing tooth according to claim 1,wherein the tooth tip is designed either symmetrical or asymmetrical.10. A short gearing tooth according to claim 9, wherein the tooth tipconsists of two roof surfaces of which both can be manufactured eitheras a plane surface or as a convex surface or of which one can bedesigned as a plane and the other as a convex surface.
 11. A shortgearing tooth according to claim 10, wherein one of the roof surfaces ismanufactured as a plane surface largely parallel to the longitudinalaxis of the tooth while the other roof surface is approximatelyinclined, forming a roof shape resembling a monopitch roof together withthe first roof surface.
 12. A short gearing tooth, comprising: a toothheight defined between a tooth base and a tooth tip as viewed along thelongitudinal axis of said tooth, said tooth tip being chamfered to forma roof having a lower surface, lateral flanks, which are undercut overat least part of their height measured along the longitudinal axis ofthe tooth, extending from the lower surface of the tooth tip roof andtapering towards the tooth base forming a relief angle ending in aradius that terminates at the tooth base, a guiding surface having anupper terminus and a lower terminus and a width defined therebetween asmeasured along the longitudinal axis of the tooth, said guiding surfacewidth being further defined as narrow or wide, said guiding surfacebeing formed on said lateral flanks between the lower edge of the roofsurface and the undercut section of the lateral flanks and being largelyparallel to the longitudinal axis of the tooth, said guiding surfacewidth being smaller than the distance along the longitudinal axis of thetooth from the upper terminus of the guiding surface to the tooth tip,and supporting surface having a lower terminus and an upper terminus anda width formed therebetween, said supporting surface being formedbetween the undercut section of the lateral flanks and the tooth baseand largely parallel to the longitudinal axis of the tooth, wherein saidnarrow guiding surface width is less than one-sixth of the distancealong the longitudinal axis of the tooth from the upper terminus of theguiding surface to the tooth tip, and wherein said wide guiding surfacewidth is less than the tooth height and greater than one-half of thedistance along the longitudinal axis of the tooth from the upperterminus of the guiding surface to the tooth tip.
 13. A short gearingtooth, comprising: a tooth height defined between a tooth base and atooth tip as viewed along the longitudinal axis of said tooth, saidtooth tip being chamfered to form a roof having a lower surface, lateralflanks, which are undercut over at least part of their height measuredalong the longitudinal axis of the tooth, extending from the lowersurface of the tooth tip roof and tapering towards the tooth baseforming a relief angle ending in a radius that terminates at the toothbase, a guiding surface having an upper terminus and a lower terminusand a width defined therebetween as measured along the longitudinal axisof the tooth, said guiding surface being formed on said lateral flanksbetween the lower edge of the roof surface and the undercut section ofthe lateral flanks and being largely parallel to the longitudinal axisof the tooth, said guiding surface width being smaller than the distancealong the longitudinal axis of the tooth from the upper terminus of theguiding surface to the tooth tip, and a supporting surface having alower terminus and an upper terminus and a width formed therebetween,said supporting surface width being further defined as low or high, saidsupporting surface being formed between the undercut section of thelateral flanks and the tooth base and largely parallel to thelongitudinal axis of the tooth, wherein said low supporting surfacewidth is greater than the width of the guiding surface and less thanless than the distance along the longitudinal axis of the tooth from thetooth base to the lower surface of the roof, and wherein said highsupporting surface width is approximately one-half the tooth height. 14.A short gearing tooth, comprising: a tooth height defined between atooth base and a tooth tip as viewed along the longitudinal axis of saidtooth, said tooth tip being chamfered to form a roof having a lowersurface, lateral flanks, which are undercut over at least part of theirheight measured along the longitudinal axis of the tooth, extending fromthe lower surface of the tooth tip roof and tapering towards the toothbase forming a relief angle ending in a radius that terminates at thetooth base, a guiding surface having an upper terminus and a lowerterminus and a width defined therebetween as measured along thelongitudinal axis of the tooth, said guiding surface width being furtherdefined as narrow or wide, said guiding surface being formed on saidlateral flanks between the lower edge of the roof surface and theundercut section of the lateral flanks and being largely parallel to thelongitudinal axis of the tooth, said guiding surface width being smallerthan the distance along the longitudinal axis of the tooth from theupper terminus of the guiding surface to the tooth tip, and a supportingsurface having a lower terminus and an upper terminus and a width formedtherebetween, said supporting surface width being further defined as lowor high, said supporting surface being formed between the undercutsection of the lateral flanks and the tooth base and largely parallel tothe longitudinal axis of the tooth, wherein said narrow guiding surfacewidth is less than one-sixth of the distance along the longitudinal axisof the tooth from the upper terminus of the guiding surface to the toothtip, and wherein said wide guiding surface width is less than the toothheight and greater than one-half of the distance along the longitudinalaxis of the tooth from the upper terminus of the guiding surface to thetooth tip, and wherein said low supporting surface width is greater thanthe width of the guiding surface and less than less than the distancealong the longitudinal axis of the tooth from the tooth base to thelower surface of the roof, and wherein said high supporting surfacewidth is approximately one-half the tooth height.